The model of stable exchanges with unbounded length, which is equivalent to the classical housing market model by [1]}, has been proposed as a possible solution concept for kidney exchange in the seminal paper by [2]}. However, when it became apparent that in the real applications the length of the cycles is limited and that the main objective is rather the maximization of the number of transplants, the literature started to focus on that sort of models [3]}.
The only research papers we are aware of about bounded length stable exchanges motivated by the kidney exchange applications are [4]} and [5]}, but these papers only considered the computational complexity (i.e., NP-hardness) of the corresponding problem.
